Hydrodynamic interactions from low to high Reynolds number

G. K. Batchelor pioneered the field of microhydrodynamics in 1970s, leading to significant advancements in this domain in the following years. Analytical techniques like renormalization and computational methods such as Stokesian Dynamics have contributed to a comprehensive understanding of hydrodynamic interactions among particles in low Reynolds number environments. Over the past few decades, these insights have found applications in various fields, including microfluidics, suspension dynamics, and microscale biophysics, such as cell motility and active matter systems. Despite these achievements, it is important to note that most progress has been limited to low Reynolds numbers. There remains a notable absence of theoretical development regarding the application of similar techniques in high Reynolds number flows. Addressing unresolved questions, such as the streamer width in suspensions of sinking fibers, may necessitate exploring regimes beyond the low Reynolds number context. My ongoing work revolve around extending existing techniques in Stokesian flow to intermediate Reynolds number, in applications such as the design of bioreactors and the modelling of phytoplanktons in the ocean.